The use of He's variational iteration method for solving a Fokker–Planck equation

Abstract

This paper applies the variational iteration method to an initial value problem of parabolic type. This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. This method is a powerful tool for solving various kinds of problems. Employing this technique, it is possible to find the exact solution or an approximate solution of the problem. Using the variational iteration method of He, a rapid convergent sequence is produced which tends to the exact solution of the problem. The results of this method are the same as with the results obtained by the Adomian decomposition method. The fact that this technique solves nonlinear equations without using Adomian polynomials can be considered as an advantage of this method over the Adomian decomposition procedure. The linear and nonlinear cases of the Fokker–Planck equation are considered and solved using the variational iteration method. To show the efficiency of the variational iteration method, several examples are presented.